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A set of nodes called vertices V accompanied with the lines
that bridge these nodes called edges E compose an explicit figure termed
as a graph G(V, E). |V (G)| = ν and |E(G)| = ε specify its order and
size respectively. A (ν, ε)-graph G determines an edge-magic total (EMT)
labeling when Γ : V (G) ∪ E(G) → {1, ν + ε} is bijective so as the
weights at every edge are the same constant (say) c i.e., for x, y ∈ V (G);
Γ(x) + Γ(xy) + Γ(y) = c, independent of the choice of any xy ∈ E(G),
such a number is interpreted as a magic constant. If all vertices gain the
smallest of the labels then an EMT labeling is called a super edge-magic
total (SEMT) labeling. If a graph G allows at least one SEMT labeling
then the smallest of the magic constants for all possible distinct SEMT labelings of G describes super edge-magic total (SEMT) strength, sm(G),
of G. For any graph G, SEMT deficiency is the least number of isolated
vertices which when uniting with G yields a SEMT graph. In this paper,
we will find SEMT labeling and deficiency of forests consisting of two
components, where one of the components for each forest is generalized
comb Cbτ (`, `, . . . , `
| {z }
τ−times
) and other component is a star, bistar, comb or path
respectively, moreover, we will investigate SEMT strength of aforesaid
generalized comb.
Salma Kanwal, Zurdat Iftikhar, Aashfa Azam. (2019) SEMT Labelings and Deficiencies of Forests with Two Components (I), , Volume 51, Issue 5.
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